Question

A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?

Answer 1

We assume the three toppings must be different.

Explanation:

Cheese : `3` choices

Toppings : `8` choices for the first, `7` for the second and `6` for the third, a total of `8xx7xx6=336`, IF the order of toppings were important -- which it isn't. This number is called the number of permutations .

Three things can be ordered in 6 ways (try this), so in the 336 permutations, there are groups of 6 that amount to the same combination :
123=132=213=231=312=321, etc.

So we have to divide the number of permutations by the number of orders to reach the number of combinations:
There are thus 336 : 6 = 56 possibilities for the toppings.

Since we need cheese AND toppings we multiply:

Number of different pizzas: 3 x 56 = 168.

Calculator : if you have the nCr function the answer would be:
3 x 8 nCr 3 = 168